Question

Below is a two-column proof incorrectly proving that the three angles of Δpqr sum to 180°. Which statement will accurately correct the two-column proof?

1) The measure of angle zry equals 180° by definition of supplementary angles.
2) Angles qry and pqr should be proven congruent after the construction of line zy.
3) The three angles of Δpqr equal 180° according to the transitive property of equality.
4) Line zy should be drawn parallel to segment qr.

Answer 1

To correct the proof that the sum of the angles in ∆pqr equals 180°, line zy should be drawn parallel to segment qr, enabling the use of alternate interior angles and corresponding angles in similar triangles.

Step-by-step explanation:

The question posed involves an incorrect two-column proof for proving that the sum of the angles in triangle ∆pqr equals 180°. The correct statement that could rectify the proof is option 4: "Line zy should be drawn parallel to segment qr." This is because if a line is drawn parallel to the base of the triangle, the alternate interior angles are congruent, which leads to establishing that the sum of the angles in ∆pqr is indeed 180° through the Angle Addition Postulate. The triangles formed by drawing such a parallel line would also be similar, allowing us to use properties of corresponding angles in similar triangles to prove the angle sum property of triangles.